Convection in the presence of a first-order phase change

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 1, 1999, Pages 539-550

  Sakurai, Shinichi ^a,b   Tschammer, Armin ^c   Pesch, Werner ^c   Ahlers, Guenter ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b KYOTO INSTITUTE OF TECHNOLOGY   (Japan)

^c UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

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ARTICLE;

EID: 18344394815     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.539     Document Type: Article

References (44)

1. See, for instance, P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993)
2. S. Chandrasekhar, Liquid Crystals (Cambridge University Press, London, 1992)
3. L. M. Blinov and V. G. Chigrinov, in Electro-optic Effects in Liquid Crystal Materials (Springer, New York, 1994).
4. A. Buka and L. Kramer, in Pattern Formation in Liquid Crystals (Springer, New York, 1996).
5. L. Kramer and W. Pesch, Annu. Rev. Fluid Mech. 27, 515 (1995).
6. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, London, 1961).
7. F. H. Busse, in The Fluid Mechanics of Astrophysics and Geophysics, Vol. 4, Mantle Convection, Plate Tectonics, and Global Dynamics, edited by W. R. Peltier (Gordon and Breach, New York, 1989).
8. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
9. For a recent review, see G. Ahlers, in Pattern Formation in Liquid Crystals (Ref. 2).
10. L.I. Berge, G. Ahlers, and D.S. Cannell, Phys. Rev. E 48, R3236 (1994).
11. E. Plaut and R. Ribotta, Europhys. Lett. 38, 441 (1997)
12. E. PlautR. RibottaPhys. Rev. E 56, R2375 (1997)
13. E. PlautR. RibottaEur. Phys. J. B 5, 265 (1998)
14. Eur. Phys. J. BE. PlautR. Ribotta5, 283 (1998).
15. L. Thomas, W. Pesch, and G. Ahlers, Phys. Rev. E 58, 5884 (1998).
16. E. Plaut and W. Pesch, Phys. Rev. E (to be published).
17. F. Busse and G. Schubert, J. Fluid Mech. 46, 801 (1971).
18. D. E. Fitzjarrald, J. Fluid Mech. 102, 85 (1981).
19. J. Salan and E. Guyon, J. Fluid Mech. 126, 13 (1983).
20. G. Ahlers, L. I. Berge, and D. S. Cannell, Phys. Rev. Lett. 70, 2399 (1993).
21. See, for instance, H. J. Kull, Phys. Rep. 206, 197 (1991), and numerous references therein.
22. G. Schubert and J. M. Straus, J. Geophys. Res. 85, 6505 (1980)
23. G. SchubertJ. M. StrausNature (London) 287, 423 (1980);[see the remark in The Fluid Mechanics of Astrophysics and Geophysics) (Ref. 5)].
24. For an interesting brief description of the current status of understanding of the mantle-convection problem, see R. A. Kerr, Science 258, 1576 (1992).
25. In the literature on two-phase convection it is customary to define the latent heat to be positive when released in the transition from the lighter to the denser phase [see The Fluid Mechanics of Astrophysics and Geophysics (Ref. 5) below Eq. 6.1].
26. G. Ahlers, D. S. Cannell, L. I. Berge, and S. Sakurai, Phys. Rev. E 49, 545 (1994).
27. We obtained our 5CB from EM Industries, 5 Skyline Drive, Hawthorne, NY 10532.
28. A. Schlüter, D. Lortz, and F. Busse, J. Fluid Mech. 23, 129 (1965).
29. See, for instance, F. Busse, J. Fluid Mech. 30, 625 (1967).
30. Q. Feng, W. Pesch, and L. Kramer, Phys. Rev. A 45, 7242 (1992).
31. See Appendix B of G. Ahlers, in Pattern Formation in Liquid Crystals (Ref. 7) for a summary of the fluid properties of 5CB.
32. For (Formula presented) we have for instance for (Formula presented) an increase of (Formula presented) roughly by a factor of (Formula presented).
33. E. Dubois-Violette, Solid State Commun. 14, 767 (1974).
34. G. Schubert and J.M. Strauss, J. Geophys. Res. 85, 6505 (1980).
35. V. S. Arpaci and P. S. Larsen, in Convection Heat Transfer (Springer, New York, 1984).
36. D. E. Hsieh and S. P. Ho, Wave and Stability in Fluids (World Scientific, Singapore, 1994).
37. D. D. Joseph and Y. Renardy, Fundamentals of Two-Fluid Dynamics I (Springer, New York, 1992).
38. R. W. Zeren and W. C. Reynolds, J. Fluid Mech. 53, 305 (1972) [see, in particular, Eqs. (21) and (22) of this reference].
39. D. A. Nield, J. Fluid Mech. 19, 341 (1964).
40. J. R. A. Pearson, J. Fluid Mech. 4, 489 (1958).
41. A. Huang and D. D. Joseph, J. Fluid Mech. 242, 235 (1992).
42. S. Faetti and V. Palleschi, J. Chem. Phys. 81, 6254 (1984).
43. For geophysical applications additional contributions in (Formula presented) and in P have to be considered (see Ref. 12).
44. A. Tschammer, Ph.D. thesis, Universität Bayreuth, Bayreuth, Germany, 1996 (unpublished).